Applied Nonlinear Dynamics

The past two decades have witnessed an explosion of ideas in the general ?eld of nonlinear dynamics. In fact, it has become increasingly clear that areas as diverse as signal processing, lasers, molecular motors, and biomedical anomalies have a c- mon underlying thread: the dynamics that underpin these systems are inh- ently nonlinear. Yet, while there has been signi?cant progress in the theory of nonlinear phenomena under an assortment of system boundary conditions andpreparations,thereexistcomparativelyfewdevicesthatactuallytakethis rich behavior into account.

This volume is intended for advanced undergraduate or first-year graduate students as an introduction to applied nonlinear dynamics and chaos. The author has placed emphasis on teaching the techniques and ideas that will enable students to take specific dynamical systems and obtain some quantitative information about the behavior of these systems. He has included the basic core material that is necessary for higher levels of study and research. Thus, people who do not necessarily have an extensive mathematical background, such as students in engineering, physics, chemistry, and biology, will find this text as useful as students of mathematics.
This new edition contains extensive new material on invariant manifold theory and normal forms (in particular, Hamiltonian normal forms and the role of symmetry). Lagrangian, Hamiltonian, gradient, and reversible dynamical systems are also discussed. Elementary Hamiltonian bifurcations are covered, as well as the basic properties of circle maps. The book contains an extensive bibliography as well as a detailed glossary of terms, making it a comprehensive book on applied nonlinear dynamical systems from a geometrical and analytical point of view.

This introduction to applied nonlinear dynamics and chaos places emphasis on teaching the techniques and ideas that will enable students to take specific dynamical systems and obtain some quantitative information about their behavior. The new edition has been updated and extended throughout, and contains a detailed glossary of terms.

This significant volume is intended for advanced undergraduate or first year graduate students as an introduction to applied nonlinear dynamics and chaos.